3x^2+42x+24=0

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Solution for 3x^2+42x+24=0 equation: 


Simplifying
3x2 + 42x + 24 = 0

Reorder the terms:
24 + 42x + 3x2 = 0

Solving
24 + 42x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(8 + 14x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(8 + 14x + x2)' equal to zero and attempt to solve:

Simplifying
8 + 14x + x2 = 0

Solving
8 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 14x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + 14x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 14x + x2 = 0 + -8
14x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
14x + x2 = -8

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = -8 + 49

Reorder the terms:
49 + 14x + x2 = -8 + 49

Combine like terms: -8 + 49 = 41
49 + 14x + x2 = 41

Factor a perfect square on the left side:
(x + 7)(x + 7) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(x + 7) equal to 6.403124237 and -6.403124237.


Subproblem 1
x + 7 = 6.403124237

Simplifying
x + 7 = 6.403124237

Reorder the terms:
7 + x = 6.403124237

Solving
7 + x = 6.403124237

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + x = 6.403124237 + -7

Combine like terms: 7 + -7 = 0
0 + x = 6.403124237 + -7
x = 6.403124237 + -7

Combine like terms: 6.403124237 + -7 = -0.596875763
x = -0.596875763

Simplifying
x = -0.596875763


Subproblem 2
x + 7 = -6.403124237

Simplifying
x + 7 = -6.403124237

Reorder the terms:
7 + x = -6.403124237

Solving
7 + x = -6.403124237

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + x = -6.403124237 + -7

Combine like terms: 7 + -7 = 0
0 + x = -6.403124237 + -7
x = -6.403124237 + -7

Combine like terms: -6.403124237 + -7 = -13.403124237
x = -13.403124237

Simplifying
x = -13.403124237


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.596875763, -13.403124237}
Solution
x = {-0.596875763, -13.403124237}

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